Professor M does Science | The Pauli matrices @ProfessorMdoesScience | Uploaded February 2023 | Updated October 2024, 2 hours ago.
💻 Book a 1:1 session: docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1
📚 The Pauli matrices are a set of three matrices of dimension 2x2 that play a crucial role in many areas of quantum mechanics. Specifically, they provide a mathematical platform to explore any quantum system described by a two-dimensional state space. Examples include spin 1/2 particles like the electron, and qubits as the fundamental unit of quantum computing. In this video, we explore some the most important mathematical properties of the Pauli matrices.
0:00 Introduction
0:54 Pauli matrices
1:54 Hermitian
3:10 Involutory
4:34 Unitary
5:10 Determinant
5:58 Trace
6:31 Eigenvalues and eigenvectors
9:27 Commutation relations
13:22 Anticommuntation relations
15:30 Wrap-up
⏮️ BACKGROUND
Hermitian operators: youtu.be/XIgDUfyrLAY
Unitary operators: youtu.be/baIT6HaaYuQ
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ
Commutator algebra: youtu.be/57xgSIV9PY0
Angular momentum: youtu.be/Bo5qoaLsBOE
⏭️ WHAT NEXT?
2x2 matrix space: youtu.be/OdYNKLULvlU
Two-state quantum systems | Eigenvalues: youtu.be/kQnQpI2B72s
Two-state quantum systems | Eigenstates: youtu.be/lkVtvdJ3GbQ
Spin 1/2: [COMING SOON]
~
Director and writer: BM
Producer and designer: MC
💻 Book a 1:1 session: docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1
📚 The Pauli matrices are a set of three matrices of dimension 2x2 that play a crucial role in many areas of quantum mechanics. Specifically, they provide a mathematical platform to explore any quantum system described by a two-dimensional state space. Examples include spin 1/2 particles like the electron, and qubits as the fundamental unit of quantum computing. In this video, we explore some the most important mathematical properties of the Pauli matrices.
0:00 Introduction
0:54 Pauli matrices
1:54 Hermitian
3:10 Involutory
4:34 Unitary
5:10 Determinant
5:58 Trace
6:31 Eigenvalues and eigenvectors
9:27 Commutation relations
13:22 Anticommuntation relations
15:30 Wrap-up
⏮️ BACKGROUND
Hermitian operators: youtu.be/XIgDUfyrLAY
Unitary operators: youtu.be/baIT6HaaYuQ
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ
Commutator algebra: youtu.be/57xgSIV9PY0
Angular momentum: youtu.be/Bo5qoaLsBOE
⏭️ WHAT NEXT?
2x2 matrix space: youtu.be/OdYNKLULvlU
Two-state quantum systems | Eigenvalues: youtu.be/kQnQpI2B72s
Two-state quantum systems | Eigenstates: youtu.be/lkVtvdJ3GbQ
Spin 1/2: [COMING SOON]
~
Director and writer: BM
Producer and designer: MC
